Theorem 1.2 (From [1]}) 
There exists a constant \(C = C_{\ref {thm:FKNP}} > 0\)  such that the following holds. Consider a non-empty ground set \(Z\)  and fix a nonempty collection of subsets \(\mathcal {H}\subseteq 2^Z\) . Suppose that there exists a \(q\) -spread probability measure on \(\mathcal {H}\) . Then \(Z(\min (Cq\log |Z|,1))\)  contains an element of \(\mathcal {H}\)  as a subset with probability \(1-o_{|Z|\rightarrow \infty }(1)\) .

